In the diagram below

m∠A = 39°

Step-by-step explanation:

From the figure attached,

BE ≅ BC

m∠C = 32°

m∠BFD = 103°

In ΔBCE,

m∠E = m∠C = 32°  [Since, BE ≅ BC]

m∠E + ∠C + m∠EBC = 180°

32° + 32° + m∠EBC = 180°

m∠EBC = 116°

m∠EBC + m∠EBA = 180° [Linear pair of angles]

116° + m∠EBA = 180°

m∠EBA = 64°

Similarly, m∠AFB + m∠DFB = 180° [Linear pair of angles]

m∠AFB + 103° = 180°

m∠AFB = 77°

Now in ΔAFB,

m∠A + m∠AFB + m∠FBA = 180° [Sum of internal angles of a triangle = 180°]

m∠A + 77° + 64° = 180°

m∠A = 39°

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